A074963 Max ( sigma(x*y) : 1<=x<=n, 1<=y<=n ).

1, 7, 13, 31, 42, 91, 96, 127, 195, 234, 234, 403, 403, 480, 576, 744, 744, 847, 847, 1170, 1344, 1344, 1344, 1651, 1860, 1860, 1860, 2240, 2240, 2880, 2880, 3048, 3048, 3048, 3048, 4368, 4368, 4368, 4368, 5040, 5040, 5952, 5952, 5952, 6552, 6552, 6552

Offset: 1

Author

Benoit Cloitre, Oct 05 2002

Keywords

• easy
• nonn

Comments

Does a(n)=sigma(n^2) for a finite number of values of n (1,2,3,4,6,8,12,18,24,60)? See A074964.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..750

Crossrefs

Cf. A000203.

Programs

Haskell

a074963 n = maximum [a000203 (x*y) | x <- [1..n], y <- [x..n]]
-- Reinhard Zumkeller, Nov 14 2011

Maple

A074963 := proc(n)
        a := 0 ;
        for x from 1 to n do
                for y from 1 to x do
                        a := max(a, numtheory[sigma](x*y)) ;
                end do:
        end do;
        a ;
end proc: # R. J. Mathar, Sep 27 2011

Mathematica

a[n_] := Module[{m = 0}, Do[m = Max[m, DivisorSigma[1, x*y]], {x, 1, n}, {y, 1, x}]; m]; Array[a, 50] (* Jean-François Alcover, Feb 12 2018 *)

PARI

a(n)=vecmax(matrix(n,n,x,y, sigma(x*y)))